Periodic, breather and rogue wave solutions for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation in fluid dynamics

Abstract

Under investigation in this paper is a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev–Petviashvili equation, which describes the propagation of nonlinear waves in fluid dynamics. Periodic wave solutions are constructed by virtue of the Hirota–Riemann method. Based on the extended homoclinic test approach, breather and rogue wave solutions are obtained. Moreover, through the symbolic computation, the relationship between the one-periodic wave solutions and one-soliton solutions has been analytically discussed, and it is shown that the one-periodic wave solutions approach the one-soliton solutions when the amplitude η→0.